There's another thing that's even weirder. I measured carefully to the bottom of the sharp V in the red weekly line. I make that about September 2nd, give or take a day or two. So the picture appears to say that from July up until the point when Hurricane Katrina hit, stocks were dropping faster than usual (going from the very top of the average range to the very bottom). Then, right around the time when Katrina hit and wasted a bunch of refineries, stocks started going up faster than usual (reaching around 25% of the way up the band). This makes no sense!

Well, I guess there is one logical possibility: Katrina's effects on demand were larger than her effects on supply. That's a pretty considerable effect!

I guess this actually makes a lot of sense looked at under an efficient market hypothesis. Stocks have reached the bottom of the band and then a bunch of refineries get wiped out. The market, well aware that stocks are low, freaks and the price goes through the roof. The market gets subsequent stock reports and sees that the price is high enough to start to finally have some impact on consumption; the price starts to drift down.
Another possibility is that consumption didn't respond much to price but did respond to the fact that a million or so (very rough guesstimate) vehicles were suddenly taken off the road, and this being the deep South, that they were on average large fuel hogs, even for our country which is addicted to fuel hogs. If the average vehicle gets 20 mpg, is driven 300 miles per week, and their are a million of them out of service, that is a demand reduction of (1 million)*(300/20)/42=almost a third of a million barrels per week.
Well, but they aren't off the road, are they? They're driving back and forth between NO and Baton Rouge...
So which are there more of? The ones submerged in New Orleans or the ones driving back and forth into the disaster zone. Additionally, upwards of half a million people are no longer commuting because they have no job.

Another question is how we measure the inventory levels. I doubt that gas in one's gas tank is counted, so the sudden dip and rebound could be explained by everybody panicing and topping off the week before Katrina hit and then not buying the following week. This is, admittedly, a short term effect, but it might explain some of this.

FWIW, I am not looking at inventory or production or consumption numbers too closely at the moment because I think that the data is suspect (at best) due to the chaos on the Gulf Coast. I rather expect the numbers will all make a lot more sense around November (barring any further shocks or chaos, of course ... my own personal force majeure clause).

Bingo! Gasoline demand is price inelastic in the short run, but it's not perfectly inelastic.

(The definition of elasticity is based on the ratio of the percentage change in demand to the percentage change in price. A ratio greater than one is elastic, a ratio less than one is inelastic. A ratio of zero (price changes but demand doesn't budge) is perfect inelasticity.)

Econbrowser had some relevant discussion a little while back. Seems to me like there might be certain psychological points where a price increase has more impact on demand than others. If it's creeping up and creeping up, people complain a little bit but don't really take much action other than not spending the money on other things that they had to spend on gasoline. But then, when it hits $3, it causes people to sit up and go "Holy s**t", and really make some change that has a significant effect on their usage.
Although, what goes into determining the gasoline stocks? What if release of the SPR is only factored into the gasoline stocks after Katrina? Wouldn't that also account for an increase in stocks?